This invention relates to teaching aids, and more particularly to a manually-operable device which simplifies the understanding of trigonometry, and specifically the understanding of and familiarization with the sine and cosine functions.
Textbook treatments of trigonometric functions necessarily employ static pictorial representations of plane triangles and curves for use in illustrating the trigonometric functions. However, the application of trigonometric principles in fields such as engineering and physics necessarily involves an understanding of such principles as applied to time-varying functions. For a proper understanding of such trigonometric functions, therefore, the student ideally should have an awareness of the relationship of the quadrants of a circle to the signs (plus or minus) of trigonometric functions, and the approximate values of the sine and cosine functions for any and all angles. Although there are some conventional mneomonic devices available to aid the students, each is designed to provide, in general, a static illustration of such relationships.
U.S. Pat. No. 2,234,896, for example, discloses a trigonometric identifier including a pair of discs rotatably mounted coaxially one above the other on a substrate. The upper disc has a pointer on its periphery and an opening for viewing any one of twenty-four different indicium printed on the face of the lower card. The lower disc also has a pointer on its periphery and when the two discs are rotated to positions in which their pointers register with certain indicia printed on the substrate, the proper answer appears beneath the opening or window in the upper disc.
U.S. Pat. No. 2,521,930 discloses a trig-meter comprising a rotatable disc mounted between two plates for manual rotation through registering finger openings in the outer plates. The disc has marked on one face a plurality of concentric circles divided into quadrants and a series of triangles, while the opposite face bears similar markings but only one circle. By rotating the disc into different angular positions various trig functions can be viewed through a plurality of differently-shaped openings in the upper plate.
Additional aids are disclosed in U.S. Pat. No. 3,042,301 and U.S. Pat. No. 3,347,458, but relate to far more complicated devices for displaying trigonometric functions.
There are currently available also, of course, electronic calculators which obviously facilitate the computation of trigonometric functions; but the visualization of these functions in relationship to a circle have been left to the student's imagination.
It is an object of this invention, therefore, to provide a relatively simple and inexpensive device for readily displaying to a student, or the like, the relationship between the angles and trigonometric functions.
Still another object of this invention is to provide a novel hand-held and operated device, which is capable readily of illustrating basic trigonometric functions relative to a circle and which is capable also of illustrating both the decimal values of such functions for given angles, and the approximate rate of change of such values with changing angles.
Other objects of the invention will be apparent hereinafter from the specification and from the recital of the appended claims, particularly when read in conjunction with the accompanying drawings.